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On Deciding Topological Classes of Deterministic Tree Languages

  • Filip Murlak
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3634)

Abstract

It has been proved by Niwiński and Walukiewicz that a deterministic tree language is either Π\(_{\rm 1}^{\rm 1}\)-complete or it is on the level Π\(_{\rm 3}^{\rm 0}\) of the Borel hierarchy, and that it can be decided effectively which of the two takes place. In this paper we show how to decide if the language recognized by a given deterministic tree automaton is on the Π\(_{\rm 2}^{\rm 0}\), the Σ\(^{\rm 0}_{\rm 2}\), or the Σ\(^{\rm 0}_{\rm 3}\) level. Together with the previous results it gives a procedure calculating the exact position of a deterministic tree language in the topological hierarchy.

Keywords

deterministic tree automata index hierarchy Borel hierarchy 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • Filip Murlak
    • 1
  1. 1.Institute of InformaticsWarsaw UniversityWarszawaPoland

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